<PAGE>
                                                                 EXHIBIT 24.1
 
                                      POWER OF ATTORNEY
                                      -----------------


        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my
attorneys-in-fact, each with full power of substitution, to sign for me as a
Director of BA Merchant Services, Inc. and file with the Securities and Exchange
Commission the Corporation's Form 10-K annual report for 1996, and any
amendments.





DATED:  March 20, 1997



                                         /s/William E. Fisher
                                         --------------------
                                            William E. Fisher



<PAGE>
 
                                    POWER OF ATTORNEY
                                    -----------------

        
        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attonorneys-in-fact, each with full power of substitution, to sign for me as a 
Director of BA Merchant Services, Inc. and file with the Securities and 
Exchange Commission the Corporation's Form 10-K annual report for 1996, and any 
amendments.




DATED:  March 20, 1997
              --




                                             /s/James G. Jones
                                             -----------------
                                                James G. Jones


















<PAGE>
 
                                POWER OF ATTORNEY
                                -----------------


        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attoneys-in-fact, each with full power of substitution, to sign for me as a 
Director and Chairman of the Board of BA MErchant Services, Inc. and file with 
the Securities and Exchange Commission the Corporation's Form 10-K annual report
for 1996, and any amendments.




DATED:  March 20, 1997
              --




                                          /s/Thomas E. Peterson
                                          ------------------------
                                             Thomas E. Peterson
                                             Chairman of the Board 

<PAGE>
 
                                POWER OF ATTORNEY
                                -----------------




        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attorneys-in-fact, each with full power of substitution, to sign for me as a 
Director of BA Merchant Services, Inc. and file with the Securities and 
Exchange Commission the Corporation's Form 10-K annual report for 1996, and 
any amendments.




DATED:  March 19, 1997



                                          /s/Barbara J. Desoer
                                          --------------------
                                             Barbara J. Desoer
 

















<PAGE>
 
                                  POWER OF ATTORNEY
                                  -----------------



        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attorneys-in-fact, each with full power of substitution, to sign for me as a 
Director of BA Merchant Services, Inc. and Corporation's Form 10-K annual report
for 1996, and any amendments.




DATED:  March 20, 1997
              --




                                              /s/Donald R. Dixon
                                              ------------------
                                                 Donald R. Dixon  
<PAGE>
 
                                    POWER OF ATTORNEY
                                    -----------------



        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attorneys-in-fact, each with full power of substitution, to sign for me as a 
Director President and Chief Executive Officer of BA Merchnt Services, Inc. and 
file with the Securities and Exchange Commission the Corporation's Form 10-K 
annual report for 1996, and any amendments.




DATE:   March 19, 1997
              --




                                              /s/Sharif M. Bayyari
                                              ----------------------
                                                 Sharif M. Bayyari
                                                 President and Chief
                                                 Executive Officer
<PAGE>
 
                                 POWER OF ATTORNEY
                                 -----------------



        I hereby appoint SUSAN LAU and CHERYL SOROKIN, and each of them, my 
attorneys-in-fact, each with full power of substitution, to sign for me as 
Executive Vice President, Chief Financial Officer and Treasurer of BA Merchant 
Services, Inc. and file with the Securities and Exchange Commission the 
Corporation's Form 10-K annual report for 1996, and any amendments.




DATED:  March 19, 1997
              --




                                          /s/James H. Williams
                                          ----------------------------  
                                             James H. Williams
                                             Executive Vice President,
                                             Chief Financial Officer,
                                             and Treasurer